{"id":"https://openalex.org/W7122677080","doi":"https://doi.org/10.1016/j.jcp.2026.114679","title":"BiLO: Bilevel Local Operator Learning for PDE Inverse Problems","display_name":"BiLO: Bilevel Local Operator Learning for PDE Inverse Problems","publication_year":2026,"publication_date":"2026-01-11","ids":{"openalex":"https://openalex.org/W7122677080","doi":"https://doi.org/10.1016/j.jcp.2026.114679"},"language":"en","primary_location":{"id":"doi:10.1016/j.jcp.2026.114679","doi":"https://doi.org/10.1016/j.jcp.2026.114679","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.jcp.2026.114679","pdf_url":null,"source":{"id":"https://openalex.org/S148709879","display_name":"Journal of Computational Physics","issn_l":"0021-9991","issn":["0021-9991","1090-2716"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-2","ki-jl-2","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational Physics","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.biorxiv.org/content/biorxiv/early/2026/01/12/2026.01.11.698923.full.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5122804443","display_name":"Ray Zirui Zhang","orcid":"https://orcid.org/0000-0002-0410-5905","observed_orcids":["https://orcid.org/0000-0002-0410-5905"]},"institutions":[{"id":"https://openalex.org/I204250578","display_name":"University of California, Irvine","ror":"https://ror.org/04gyf1771","country_code":"US","type":"education","lineage":["https://openalex.org/I204250578"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ray Zirui Zhang","raw_affiliation_strings":["Department of Mathematics, University of California, Irvine"],"raw_orcid":"https://orcid.org/0000-0002-0410-5905","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California, Irvine","institution_ids":["https://openalex.org/I204250578"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036077055","display_name":"Christopher E. Miles","orcid":"https://orcid.org/0000-0001-5494-403X","observed_orcids":["https://orcid.org/0000-0001-5494-403X"]},"institutions":[{"id":"https://openalex.org/I204250578","display_name":"University of California, Irvine","ror":"https://ror.org/04gyf1771","country_code":"US","type":"education","lineage":["https://openalex.org/I204250578"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Christopher E. Miles","raw_affiliation_strings":["Department of Mathematics, University of California, Irvine"],"raw_orcid":"https://orcid.org/0000-0001-5494-403X","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California, Irvine","institution_ids":["https://openalex.org/I204250578"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084618257","display_name":"Xiaohui S. Xie","orcid":"https://orcid.org/0000-0002-5479-6345","observed_orcids":["https://orcid.org/0000-0002-5479-6345","https://orcid.org/0000-0002-2879-6464","https://orcid.org/0000-0001-9413-4461"]},"institutions":[{"id":"https://openalex.org/I204250578","display_name":"University of California, Irvine","ror":"https://ror.org/04gyf1771","country_code":"US","type":"education","lineage":["https://openalex.org/I204250578"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xiaohui Xie","raw_affiliation_strings":["Department of Computer Science, University of California, Irvine"],"raw_orcid":"https://orcid.org/0000-0002-5479-6345","affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of California, Irvine","institution_ids":["https://openalex.org/I204250578"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010714351","display_name":"John S. Lowengrub","orcid":"https://orcid.org/0000-0003-1759-0900","observed_orcids":["https://orcid.org/0000-0003-1759-0900"]},"institutions":[{"id":"https://openalex.org/I204250578","display_name":"University of California, Irvine","ror":"https://ror.org/04gyf1771","country_code":"US","type":"education","lineage":["https://openalex.org/I204250578"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"John S. Lowengrub","raw_affiliation_strings":["Department of Biomedical Engineering, University of California, Irvine","Department of Mathematics, University of California, Irvine"],"raw_orcid":"https://orcid.org/0000-0003-1759-0900","affiliations":[{"raw_affiliation_string":"Department of Biomedical Engineering, University of California, Irvine","institution_ids":["https://openalex.org/I204250578"]},{"raw_affiliation_string":"Department of Mathematics, University of California, Irvine","institution_ids":["https://openalex.org/I204250578"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5010714351","https://openalex.org/A5122804443"],"corresponding_institution_ids":["https://openalex.org/I204250578"],"apc_list":{"value":3980,"currency":"USD","value_usd":3980},"apc_paid":null,"fwci":6.3185,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.94249002,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"551","issue":null,"first_page":"114679","last_page":"114679"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9814000129699707,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9814000129699707,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.011800000444054604,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.0017000000225380063,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bi-level-optimization","display_name":"bi-level optimization","score":0.9980000257492065},{"id":"https://openalex.org/keywords/neural-network-surrogate-model","display_name":"neural network surrogate model","score":0.37400001287460327},{"id":"https://openalex.org/keywords/descent-direction","display_name":"descent direction","score":0.44699999690055847},{"id":"https://openalex.org/keywords/auxiliary-variables","display_name":"auxiliary variables","score":0.6549999713897705},{"id":"https://openalex.org/keywords/sparse-noisy-data","display_name":"sparse noisy data","score":0.6079999804496765}],"concepts":[{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.6189000010490417},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.5882999897003174},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5734000205993652},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5403000116348267},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5376999974250793},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.5128999948501587},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.4830000102519989},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4521999955177307},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44110000133514404},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.42399999499320984},{"id":"https://openalex.org/C3309286","wikidata":"https://www.wikidata.org/wiki/Q4907693","display_name":"Bilevel optimization","level":3,"score":0.41280001401901245},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.41260001063346863},{"id":"https://openalex.org/C157553263","wikidata":"https://www.wikidata.org/wiki/Q5168004","display_name":"Coordinate descent","level":2,"score":0.39079999923706055},{"id":"https://openalex.org/C53846429","wikidata":"https://www.wikidata.org/wiki/Q186475","display_name":"Partial derivative","level":2,"score":0.37929999828338623},{"id":"https://openalex.org/C116149140","wikidata":"https://www.wikidata.org/wiki/Q2070951","display_name":"Descent direction","level":4,"score":0.3783000111579895},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37049999833106995},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.35580000281333923},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3296999931335449},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3237000107765198},{"id":"https://openalex.org/C6180225","wikidata":"https://www.wikidata.org/wiki/Q3411771","display_name":"Penalty method","level":2,"score":0.31529998779296875},{"id":"https://openalex.org/C165551260","wikidata":"https://www.wikidata.org/wiki/Q4428962","display_name":"Adjoint equation","level":3,"score":0.30730000138282776},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2964000105857849},{"id":"https://openalex.org/C2011187","wikidata":"https://www.wikidata.org/wiki/Q383851","display_name":"Directional derivative","level":2,"score":0.2944999933242798},{"id":"https://openalex.org/C70915906","wikidata":"https://www.wikidata.org/wiki/Q1058681","display_name":"Differential operator","level":2,"score":0.2759000062942505},{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.2639999985694885}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1016/j.jcp.2026.114679","doi":"https://doi.org/10.1016/j.jcp.2026.114679","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.jcp.2026.114679","pdf_url":null,"source":{"id":"https://openalex.org/S148709879","display_name":"Journal of Computational Physics","issn_l":"0021-9991","issn":["0021-9991","1090-2716"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-2","ki-jl-2","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational Physics","raw_type":"journal-article"},{"id":"doi:10.64898/2026.01.11.698923","doi":"https://doi.org/10.64898/2026.01.11.698923","is_oa":true,"landing_page_url":"https://doi.org/10.64898/2026.01.11.698923","pdf_url":"https://www.biorxiv.org/content/biorxiv/early/2026/01/12/2026.01.11.698923.full.pdf","source":{"id":"https://openalex.org/S4306402567","display_name":"bioRxiv (Cold Spring Harbor Laboratory)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I2750212522","host_organization_name":"Cold Spring Harbor Laboratory","host_organization_lineage":["https://openalex.org/I2750212522"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"bioRxiv","raw_type":"posted-content"},{"id":"pmh:oai:arXiv.org:2404.17789","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2404.17789","pdf_url":"https://arxiv.org/pdf/2404.17789","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2404.17789","doi":"https://doi.org/10.48550/arxiv.2404.17789","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2404.17789","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.64898/2026.01.11.698923","doi":"https://doi.org/10.64898/2026.01.11.698923","is_oa":true,"landing_page_url":"https://doi.org/10.64898/2026.01.11.698923","pdf_url":"https://www.biorxiv.org/content/biorxiv/early/2026/01/12/2026.01.11.698923.full.pdf","source":{"id":"https://openalex.org/S4306402567","display_name":"bioRxiv (Cold Spring Harbor Laboratory)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I2750212522","host_organization_name":"Cold Spring Harbor Laboratory","host_organization_lineage":["https://openalex.org/I2750212522"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"bioRxiv","raw_type":"posted-content"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G278443292","display_name":null,"funder_award_id":"594598, QN","funder_id":"https://openalex.org/F4320306164","funder_display_name":"Simons Foundation"},{"id":"https://openalex.org/G2981664957","display_name":"CAREER: Learning stochastic spatiotemporal dynamics in single-molecule genetics","funder_award_id":"2339241","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6671297155","display_name":null,"funder_award_id":"CAREER","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6791967163","display_name":null,"funder_award_id":"DMS176\u20103272","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6840471226","display_name":"NSF-Simons Center for Multiscale Cell Fate Research","funder_award_id":"1763272","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8476859885","display_name":"Collaborative Research: : Mathematical modeling and computation of morphological instabilities in reactive fluids driven out of equilibrium","funder_award_id":"2309800","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306164","display_name":"Simons Foundation","ror":"https://ror.org/01cmst727"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7122677080.pdf","grobid_xml":"https://content.openalex.org/works/W7122677080.grobid-xml"},"referenced_works_count":86,"referenced_works":["https://openalex.org/W1538120041","https://openalex.org/W1855169650","https://openalex.org/W1977822596","https://openalex.org/W1987869189","https://openalex.org/W2019438752","https://openalex.org/W2046465662","https://openalex.org/W2082261407","https://openalex.org/W2114424556","https://openalex.org/W2125916088","https://openalex.org/W2149498546","https://openalex.org/W2157358125","https://openalex.org/W2899283552","https://openalex.org/W2919520822","https://openalex.org/W2948551291","https://openalex.org/W2949650786","https://openalex.org/W2957969499","https://openalex.org/W2964121744","https://openalex.org/W2979786244","https://openalex.org/W2993158195","https://openalex.org/W3010849941","https://openalex.org/W3041129870","https://openalex.org/W3043516796","https://openalex.org/W3087129589","https://openalex.org/W3092923133","https://openalex.org/W3116268267","https://openalex.org/W3116689020","https://openalex.org/W3128157635","https://openalex.org/W3154575637","https://openalex.org/W3155333505","https://openalex.org/W3163993681","https://openalex.org/W3167823354","https://openalex.org/W3180558463","https://openalex.org/W3184908771","https://openalex.org/W3185042346","https://openalex.org/W3194436063","https://openalex.org/W3197732874","https://openalex.org/W3198653666","https://openalex.org/W3200673624","https://openalex.org/W3201666041","https://openalex.org/W3209909540","https://openalex.org/W3210300097","https://openalex.org/W3212555946","https://openalex.org/W4205205982","https://openalex.org/W4213444041","https://openalex.org/W4221019179","https://openalex.org/W4221158602","https://openalex.org/W4224089288","https://openalex.org/W4225906496","https://openalex.org/W4226286712","https://openalex.org/W4280607878","https://openalex.org/W4287671439","https://openalex.org/W4293803871","https://openalex.org/W4296540988","https://openalex.org/W4297847137","https://openalex.org/W4307154444","https://openalex.org/W4308979219","https://openalex.org/W4313172816","https://openalex.org/W4318350421","https://openalex.org/W4361865663","https://openalex.org/W4362581027","https://openalex.org/W4380841400","https://openalex.org/W4380992163","https://openalex.org/W4384207653","https://openalex.org/W4385198556","https://openalex.org/W4385965970","https://openalex.org/W4386857800","https://openalex.org/W4386859252","https://openalex.org/W4386955678","https://openalex.org/W4387618874","https://openalex.org/W4388870165","https://openalex.org/W4389067443","https://openalex.org/W4390569755","https://openalex.org/W4390753291","https://openalex.org/W4390839314","https://openalex.org/W4391418547","https://openalex.org/W4391505477","https://openalex.org/W4392004327","https://openalex.org/W4392620300","https://openalex.org/W4394862890","https://openalex.org/W4405318319","https://openalex.org/W4407181882","https://openalex.org/W4411880714","https://openalex.org/W4412884603","https://openalex.org/W4414431828","https://openalex.org/W7123335278","https://openalex.org/W7128436957"],"related_works":["https://openalex.org/W4318350421","https://openalex.org/W3000220657","https://openalex.org/W7213625918","https://openalex.org/W7123335278","https://openalex.org/W4379379581","https://openalex.org/W4220816679","https://openalex.org/W4390753291","https://openalex.org/W3122676996","https://openalex.org/W7102626244","https://openalex.org/W4408934197"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2}],"updated_date":"2026-10-31T12:09:11.096373","created_date":"2026-01-13T00:00:00"}